Differential equation (to solve analytically)

[dragonblood]

(x^2+1)y'=x^2+x-1+4xy



How can I solve this equation analytically?



I have almost no idea. I thought that y might be a series.....please help :)
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution

[HallsofIvy]

If you write that as (x^2+ 1)dy/dx- 4xy= x^2+ x- 1 or
\frac{dy}{dx}- \frac{4x}{x^2+ 1}y= \frac{x^2+ x- 1}{x^2+ 1}[/itex]
a linear differential equation. Then
[tex]e^{\int {4x}{x^2+1} dx} is an integrating factor. Multiplying the entire equation by it will make the left side an "exact" derivative.

[djeitnstine]

Let me just clarify that integrating factor for you ivy =] e^{- \int \frac{4x}{x^2+1} dx}

[dragonblood]

Allright :) Thanks peeps!

[HallsofIvy]

Dang! Dropped a sign, didn't I?